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The random effects approach in meta-analysis due to DerSimonian and Laird is well established and used pervasively. It has been established by Brockwell and Gordon that this method, when used for confidence intervals, leads to coverage probabilities lower than the nominal value. A number of alternatives have been proposed, but these either have the defect of iterative and complicated calculation, or deficient coverage. In this paper we propose a new approach, which is simple to use, and has coverage probabilities better than the alternatives, based on extensive simulation. We call this approach the 'quantile approximation' method.
Brockwell et al. (Mon,) studied this question.
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